Measuring modal content of multi-moded fibers

ABSTRACT

The output modal content of optical fibers that contain more than one spatial mode may be analyzed and quantified by measuring interference between co-propagating modes in the optical fiber. By spatially resolving the interference, an image of the spatial beat pattern between two modes may be constructed, thereby providing information about the modes supported by the optical fiber. Measurements of the phase front exiting the optical fiber under test are advantageously performed in the far field.

RELATED APPLICATION

This application is a Continuation-In-Part of application Ser. No.12/214,629 filed Jun. 20, 2008, claiming the benefit of U.S. ProvisionalApplication No. 61022626, filed Jan. 22, 2008, which applications areincorporated herein by reference.

FIELD OF THE INVENTION

This invention relates to analyzing the optical properties of opticalwaveguides. More specifically it relates to methods and apparatus formeasuring mode patterns and power levels in multi-mode optical fibers.

BACKGROUND OF THE INVENTION

Optical fiber lasers are desirable for their excellent beam quality,even when operating at high power. The quality of a beam emitted from anoptical fiber is frequently quantified using the measure “M²”, which isa measure of how tightly the beam can be focused in free space. A beamwith a perfect Gaussian spatial profile has a theoretical M² value ofone. A problem with applying M² measurements to optical fibers is thatlarge mode area fibers typically support several modes, and M² can berelatively insensitive to the amount of power in a higher order mode. M²is even less useful, and potentially confusing, when propagation in ahigher order mode (HOM) is intentional, as individual HOMs haveinherently high values of M². Therefore new measurement techniquescapable of quantifying the modal content of fibers that support morethan one mode are needed.

SUMMARY OF THE INVENTION

We have developed a technique for analyzing and quantifying the outputmodal content of optical fibers that support more than one spatial mode.The technique is based on measuring interference between co-propagatingmodes in the optical fiber. By spatially resolving the interference, animage of the spatial beat pattern between two modes is constructed, thusproviding information about the modes that are propagating in theoptical fiber.

BRIEF DESCRIPTION OF THE DRAWING

The invention may be more easily understood with the aid of the drawing,in which:

FIGS. 1 and 2 show experimental setups for spatially resolved spectralinterferometry measurements useful for characterizing modal content ofmulti-mode fibers. The arrangement of FIG. 1 has an imaging lensarrangement for focus and magnification. The measurement apparatus ofFIG. 2 is designed for proximity measurements;

FIG. 3 is a plot of wavelength vs. power showing an output lightintensity spectrum measured at detector 19 in FIG. 1 or 2;

FIG. 4 shows the Fourier transform of the spectrum of FIG. 3;

FIG. 5 is a beam profile obtained by integrating the spectrum at eachx,y, point using the measurement apparatus of FIG. 1 or 2;

FIG. 6 is a power spectrum derived by Fourier transforming datacollected from measurements illustrated in FIGS. 5 and 7-10;

FIGS. 7-10 are images and relative power levels of higher-order modesobtained using the measurement apparatus of FIG. 1 or 2;

FIG. 11 is an alternative measurement apparatus for adding measurementsof spatially resolved coherence; and

FIGS. 12 and 13 show experimental setups, similar to that of FIG. 1, forspatially resolved spectral interferometry measurements in the farfield.

DETAILED DESCRIPTION

In the context intended for this discussion, the subject optical fibersare typically few mode fibers but are referred to here as multi-modefibers. In typical applications wherein specific modes arecharacterized, the number of modes propagating in the optical fiber maybe few. However, applications may arise where the optical fiber supportsmany modes but just one, or a few, or even mode groups, may be thesubject of the analysis. In some situations, the fiber may be nominallysinglemode and a method is desired to analyze the characteristics ofweakly guided or weakly radiated higher order modes.

A schematic of one particular implementation of the measurementtechnique of the invention is illustrated in FIG. 1. Light from anoptical source 11, having a broad bandwidth (few tens of nanometers, ormore) such as an amplified spontaneous emission source (ASE), islaunched into an optical fiber 12. The optical fiber 12 is the fiberunder test and is typically a large-mode-area (LMA) fiber that supportsmultiple transverse modes. At the exit of the fiber, the light isre-imaged onto the tip of single mode fiber 18. The light collected bythe single mode fiber is measured using detector 19, which in theembodiment shown is an optical spectrum analyzer (OSA). The imagingsystem used in this embodiment comprises imaging lenses 14 and 16, and apolarizer 15. The polarizer 15 ensures polarization mode alignment andthe single mode fiber 18 ensures modal overlap in the OSA. If desired,the focal lengths of the imaging lenses can be chosen to magnify theimage. If the optical fiber being analyzed is polarization maintaining,the polarizer may not be necessary. However a polarizer may still beused to analyze any residual light launched into the non-desiredpolarization state.

In a slightly modified alternative embodiment, shown in FIG. 2, theimaging lenses are removed, and the single mode fiber is placed in closeproximity to the LMA fiber. In both setups fiber ends may be cleaved,polished, or even connectorized. It may be inferred from comparing FIGS.1 and 2 that the polarizing element may be placed at any point betweenthe output of the LMA fiber and the detector.

If the light exiting the LMA fiber is single moded, then the spectrummeasured by the OSA simply reflects the power spectrum of the broadbandsource. However, if multiple modes are propagating in the LMA fiber,they will each have slightly different group delays and consequentlywill interfere at the output of the fiber. As a result, a spectralinterference pattern, related to the beating of the modes, is measuredin the OSA.

The single mode probe fiber is assumed to sample only a small portion ofthe near-field image of the beam from the fiber under test. Thereforethe end of the single mode fiber may be placed on a scanning X-Y stage17 (FIGS. 1 and 2) and the position of the fiber end is raster scannedwith respect to the position of the beam and at each x and y position ofthe single mode fiber tip an optical spectrum is measured. FIG. 3 showsa representative measurement of the spectrum from the single mode fiberat an arbitrary (x,y) point. The spectrum shows clearly visible modebeats. By Fourier transforming the spectrum with respect to opticalfrequency the spectrum of FIG. 4 results. The spectrum in FIG. 4 showswell defined peaks, with each peak corresponding to beating between adifferent set of modes. Therefore, by measuring the spectrum at each xand y point, and Fourier filtering, the spatial pattern of the beatbetween two different transverse modes can be obtained. The measurementsprovide information for both identification of the modes propagating inthe fiber, and quantification of the relative power in each mode.

To demonstrate the measuring method of the invention, results from a 20μm mode-field diameter, Yb doped fiber are given. The measurements wereobtained using the set up shown in FIG. 1, with a 6 m length of LMAYb-doped fiber, and an Yb amplified spontaneous emission (ASE) sourcefor broadband input light. Imaging lenses magnified the near-field imageof the beam, and 980-nm single mode fiber (SMF) was used as a probefiber. The SMF was raster scanned in x and y, and a set of 32×32 opticalspectra were collected.

When the optical spectrum at each (x,y) point is integrated, an image ofthe beam profile is obtained from the data. This image is shown in FIG.5, showing a primarily Gaussian shaped mode. The M² of this fiber wasmeasured to be approximately 1.1. This value for M² is consistent withthe value for M² predicted for the fundamental LP01 mode.

The spectrum at each point was Fourier transformed, and all of themeasured spectra were averaged together to give the plot shown in FIG.6. Although most of the optical power in the fiber is contained in thefundamental, LP₀₁, mode, multiple beat frequencies clearly indicate thepresence of more than one higher order mode.

To quantify the modal content the value of the Fourier transform at agiven Fourier frequency was recorded for every (x,y) point, andnormalized to the value of the Fourier transform at zero frequency asdescribed below in the discussion of data analysis. This calculationgives the strength of the interference term between the two modes. Fromthis term the relative strength of the two fields and spatial pattern isobtained.

Results for the strongest of the peaks visible in the Fourier transformof the spectrum are shown in FIGS. 7-10. For example, when the Fouriertransform is filtered at the peak labeled ‘c’ in FIG. 6, the resultingcalculation shows an image (FIG. 7) of an LP₀₂ mode, with a power of 24dB weaker than the power contained in the fundamental mode. Two closelyspaced peaks labeled ‘d’ (FIG. 8) and ‘e’ (FIG. 9) both correspond toLP₁₁ modes, but the two are rotated with respect to each other by 90degrees. The peak labeled ‘d’ is the strongest observedhigher-order-mode, with a power 15.5 dB down from the power in thefundamental mode. The image of the mode with beat frequencycorresponding to ‘f’ (FIG. 10) clearly shows an LP₂₁ mode with power 29dB down from the fundamental mode. Other modes with even weaker powerare also visible as additional peaks.

As should be evident this measurement method readily identifies themodes propagating in the fiber while also quantifying the level of modalmultipath interference (MPI).

The mode image and MPI from the Fourier transform can be determinedusing the following.

Two beam interference between electric fields with amplitudes A₁(x,y,ω)and A₂(x,y,ω) is considered. If both fields are assumed to have the samefrequency dependence than the two fields are related by

A ₂(x,y,ω)=α(x,y)A ₁(x,y,ω).

When the two fields interfere on a detector the resulting spectralintensity is

I(x,y,ω)=I ₁(x,y,ω)[1+α²(x,y)+2α(x,y) cos(αω)],

where the phase difference between the two modes, aω, is assumed to be alinear function in frequency. By integrating the measured spectralintensity over ω, I₁(x,y) and I₂(x,y) are related to the total spectralintensity by

${{I_{1}\left( {x,y} \right)} = \frac{I\left( {x,y} \right)}{1 + {\alpha^{2}\left( {x,y} \right)}}},{and}$${I_{2}\left( {x,y} \right)} = {\frac{{\alpha^{2}\left( {x,y} \right)}{I\left( {x,y} \right)}}{1 + {\alpha^{2}\left( {x,y} \right)}}.}$

This assumes that the many periods of the beat frequency are containedwithin the measurement window of the spectrometer, and that I₁(x,y,ω) isslowly varying in frequency. The total MPI is the ratio of the twointensities, integrated over the beam.

${MPI} = {10{{\log \left\lbrack \frac{\int{\int{{I_{2}\left( {x,y} \right)}{x}{y}}}}{\int{\int{{I_{1}\left( {x,y} \right)}{x}{y}}}} \right\rbrack}.}}$

Experimentally, the measurement of MPI is made by extracting thequantity α(x,y) from the Fourier transform of the measured spectralintensity, I(x,y,ω). The Fourier transform of I(x,y, ω) with respect toω is

{I(x,y,ω)}=B(x,y,u)=(1+α²)B ₁(x,y,u)+α(B ₁(x,y,u−α)+B ₁(x,y,u+α)),

where u is the Fourier transform coordinate of ω, and B₁(x,y,u) is theFourier transform I₁(x,y,ω). Assuming the peaks are well separated, theratio of the peaks at u=0 to u=a is therefore

$\frac{B\left( {x,y,{u = a}} \right)}{B\left( {x,y,{u = 0}} \right)} = {{f\left( {x,y} \right)} = \frac{\alpha \left( {x,y} \right)}{1 + {\alpha^{2}\left( {x,y} \right)}}}$

The fraction f(x,y) is calculated from the ratios of the value of theFourier transformed spectral intensity at the desired spectral peak tothe DC value. From f(x,y), α(x,y) can be calculated at each (x,y) point:

${\alpha \left( {x,y} \right)} = \frac{1 - \sqrt{1 - {4{f^{2}\left( {x,y} \right)}}}}{2{f\left( {x,y} \right)}}$

Note that the above algorithm deals with extracting the intensityprofile of the mode. Higher order modes in fibers also contain uniquephase profiles. For example the two lobes of the LP₁₁ mode have a piphase difference between them. The phase difference between the modes isreadily obtainable from the data from the Fourier transform.Consequently by simply Fourier transforming the optical spectra at eachx-y point and making note of the phase at a given Fourier frequency,phase images of higher order modes can be obtained.

A generalized measurement setup may be described as basically that shownin FIGS. 1 and 2 except that the detector may be a detector withfrequency resolution matched to the optical source. A computer may beused to perform automated scanning of the spatial filter, and dataacquisition from the detector. The near field image of the fiber may bemagnified using imaging optics (FIG. 1) or the spatial filter may beplaced in close proximity to the fiber output (FIG. 2). In either case,for achieving good spatial resolution the spatial filter is preferablysmaller than the spatial features of the optical mode.

Polarization overlap at the detector is desirable. A polarizer in thebeam forces polarization overlap. If the modes are not alreadyco-polarized, measurements may be made with two different alignments ofthe polarizer to quantify the MPI and relative polarizations of themodes.

In the experiments described above, a single-mode fiber was used tosample a small portion of the beam from the fiber under test.Alternatively, a pinhole with imaging optics to couple the light fromthe pinhole to the OSA may be used.

A variety of alternatives exist for the combination of broadband opticalsource and detector. For characterization of long fibers it may beuseful to operate the method in the electrical domain, with a DFB laseras a broadband source (for example) and a photodiode plus RF electricalspectrum analyzer to obtain frequency resolution. A laser with frequencytunability coupled with a power meter or photodetector providesbroadband operation and high frequency resolution. For even simpleroperation, a tunable laser, serving as a broadband source, plus acamera, such as a CCD, provides a simple setup and eliminates the needfor a separate spatial filter element. Other alternative arrangementsare:

-   -   1. using a bulk optic spatial filter, rather than an SMF fiber        in front of the optical detector;    -   2. as an alternative to scanning the position of the spatial        filter, the beam may be translated in the focal plan by scanning        the position of the end-face of the multi-mode fiber under test,        scanning the focusing or collimating optics, or using a turning        mirror or lens that can be suitably tilted;    -   3. using computers and/or application specific ICs or circuit        boards for automated data acquisition and hardware control of        the optical source, optical detection, and or scanning        equipment;    -   4. using a computer and software algorithm to process the data        and calculate the MPI levels of the various modes. A suitable        algorithm for analyzing the data is described above, but it is        recognized that there are many possible computer algorithms for        analyzing the data.

All these methods share the common function of sampling sequentialportions of the output test beam by sampling a portion of the beam fromthe fiber under test and analyzing the sequential portions using anoptical detector. Sequential portions are portions in space, typicallyx-y space, that are sequentially analyzed as a function of frequency. Insome embodiments the broadband source emits a band of wavelengths andthe frequency dependence of the transmission through the fiber undertest is analyzed using an optical detector with frequencydiscrimination. In other embodiments the frequency dependence of thetransmission through the fiber under test is analyzed by tuning abroadband source through a band containing individual wavelengths andmeasuring the power of the source at each individual wavelength.

In the technique described above the multi-mode fiber to becharacterized functions as an interferometer in which low powers inunwanted modes are generated at a few discrete scattering points such asat splices or at the launch into the fiber. Because the measurementrelies on a well defined Fourier peak it is dependant on discretemulti-path interference (MPI). MPI is defined as the ratio of powerbetween two modes in a dB scale. The technique is most effective whenmultiple higher order modes are generated by scattering at a fewdiscrete sites in the fiber under test, for example, at splices or atthe insertion point of the fiber. Another aspect, however, isdistributed MPI, in which modes are generated through scatteringcontinuously along the fiber length. Distributed MPI can also bequantified with this technique, and is identifiable as it creates abroad plateau in the frequency spectrum for the mode beats, rather thanthe sharp peak caused by discrete scattering. Incoherent light, such asthat produced by ASE in an amplifier, may also be more difficult toquantify by the measurement described above. To address this, the methodmay be modified by quantifying the coherence of the fundamental mode ofthe fiber.

FIG. 11 is a schematic of a suitable setup for the modified measurement.The optical fiber to be characterized and the scanning spatial filterare placed in one arm of a Mach-Zender interferometer. A single modefiber 41, a variable delay element 42, and polarization control means 43are placed in the other arm. The variable delay allows the group delaybetween the desired mode of the fiber under test and the single mode armof the interferometer to be placed at an arbitrary offset. Incoherentlight in modes other than the mode to be characterized produces aspatial pattern in the coherence of the mode. Polarization controlproduces polarization overlap at the output of the interferometer, whilethe spatial filter, here shown as a single-mode fiber, ensures modaloverlap at each (x,y) point.

It is evident from the foregoing description, and the embodimentrepresented generally by FIG. 1, that it is convenient to measure thespatially dependent interference pattern of the output beam from thespatial filter, in this case a few mode fiber, in the near field, i.e.,in the image plane of the optical system used for imaging the output ofthe fiber under test. With this measurement method, the phase front ofthe beam exiting the end surface of the optical fiber is planar.However, effective measurements may also be made in the far field. Thisfollows from the independent discovery that when the output beam fromthe spatial filter undergoes diffraction into the far field, and thephase front develops a curvature, all the modes have undergone anequivalent Fourier transform and the mode relationship along the curvedphase front is representative of that along the x-y plane at the nearfield output of the spatial filter.

FIGS. 12 and 13 show experimental setups, similar to that of FIG. 1, forspatially resolved spectral interferometry measurements in the farfield. FIG. 12 shows the output of the optical fiber under test 12diffracting into the far field. The phase front in the far field iscurved as shown. A detector 18,19, with wavelength resolution is usedthat effectively scans the output along a suitable arc 51. The detectormay be, for example, the tip of an optical fiber moving in an arc. Thefigure shows the scan in one dimension but it will be understood thatthe scan actually proceeds in two dimensions. The simplest scan mode isone where the detector remains equidistant from the optical fiber outputduring the scan. That results, for example, when the detector scans overa spherical arc and the focal point of the spherical arc is at or nearthe optical fiber end. Using multiple detectors in a spherical array,for example, a photodiode array, removes the need for moving elements.The photodiode array may be an array of simple photodiodes withoutwavelength resolution. The wavelength spectrum in this case may begenerated with a tunable wavelength source.

As mentioned earlier a CCD imaging device is a desirable alternative,and removes the need for moving elements. In that case the entire x-ydependence of the intensity of the beam at a single wavelength ismeasured at once, and thus provides a fast response. However, thischoice of measurement requires a tunable laser to produce a wavelengthspectrum. The stability of the tunable laser may become an issue. Driftin the wavelength of the laser during the measurement may causeinaccurate results. In contrast, measuring pixels individually with ascanning fiber probe, for instance in the method described by FIG. 12,has relaxed requirements in terms of the phase stability between variousmodes in the fiber. To measure the frequency of the spectral beat notethe phase between modes should be stable during the duration of theoptical spectrum measurement. However, since the relevant data is theamplitude of the spectral beat note for a given individual pixel, driftof the phase between the modes from one pixel to another may betolerated when the beam is measured using a scanning fiber probe.

When the beam is measured using a CCD, all the pixels are measured atonce, then the wavelength of the tunable laser is incremented and thebeam is measured again. In this configuration, the phases between themodes should therefore remain stable for the duration of the entiremeasurement. Assuming a CCD camera that acquires 10 frames per second,for example, with 1000 wavelength points being measured, the phasesshould remain stable for 100 seconds.

In an alternative method of using multiple detectors in a sphericalarray, the photodiode array may be an array of simple individualphotodiodes wired to a data acquisition device.

Another alternative to moving the detector is to move the light beamexiting from the optical fiber output using beam steering optics to scanthe beam in a raster over a stationary detector. Beam steering opticsfor raster scanning may be refractive or reflective.

Another option is represented by FIG. 13, where the scan of the opticalbeam from the optical fiber 12 is implemented in an x-y plane. FIG. 13shows the detector scanning in x-y plane 61. Since the distance 62between the phase front and the x-y plane varies, a correction factor isused in conjunction with the detector to compensate for the varyingdistance.

Other options for detecting in variations in the optical output alongthe curved far field phase front may occur to those skilled in the art.The far field is where the beam has undergone substantial diffraction.In the far field, the spatial intensity profile of the beam is thespatial Fourier Transform of the intensity profile at the exit from theoptical fiber. As the beam diffracts it typically will have a curvedphase front. A substantially curved phase front is easily discerned byoptical elements, detector elements, or software, in the measuringmethod that compensate for curvature in the phase front of the opticalbeam being measured.

To increase diffraction of the output test beam, or otherwise shape thebeam in the far field, a suitable lens or lens system may be inserted ator near the output of the optical fiber under test. Optical lens systemsmay be designed that produce a planar wave front in the far field.

Multimode fiber that is the subject of the foregoing description can berecognized as generally having a relatively large core diameter,typically greater than 10 microns. This property distinguishes theoptical fiber from single mode optical fiber that typically has a corediameter of 6 microns or less. A multi-mode optical fiber in the contextof the invention is an optical fiber that supports more than onetransverse mode.

Light propagating in an optical fiber generates a group delay differencebetween the modes which have a beat frequency in the optical spectralequal to 1/(group delay difference). The optical fiber length should belong enough to produce a beat frequency which is at half the opticalbandwidth of the source being used. The optical fiber length should beshort enough that the beat frequency is at least twice the resolutionbandwidth of the optical detector being used.

A broadband source is defined as a light source having a wavelengthbroader than at least twice the beat frequency of the group delaydifference to be characterized. The beat frequency between the modes isdetermined as 1/(difference in group delay between the modes). Thebroadband source may be a device that emits light over a broadwavelength band or a device that can be tuned to several or manywavelengths over a broad wavelength band. In the former case, afrequency selective detector is used to discriminate wavelengths at thedetection end. In the latter case the frequency selection is made at theinput end, and a wavelength selective detection means is not need at thedetection end.

The invention has been described in the context of optical fibers, andthis context is expected to be the most relevant in commercial practice.However, the principles apply to other forms of optical waveguides, forexample, waveguides in planar optical integrated circuits.

In summary the method of the invention involves the steps of passinglight from a broadband source through a length of multi-mode waveguideunder test to produce an output test beam, and analyzing discreteportions of the output test beam using a photodetector located in thenear field or far field. The portion of the test beam may be generatedusing a single mode fiber to sample a portion of the beam from the fiberunder test and scanning the single mode fiber in the x-y plane, with thex-y plane approximately normal to the direction of the test beam. Or thewave front of the output test beam may be measured in the far field asdescribed above.

In concluding the detailed description, it should be noted that it willbe obvious to those skilled in the art that many variations andmodifications may be made to the preferred embodiment withoutsubstantial departure from the principles of the present invention. Allsuch variations, modifications and equivalents are intended to beincluded herein as being within the scope of the present invention, asset forth in the claims.

1. A method for characterizing the modes propagating in an opticalwaveguide comprising the steps of: passing light from a broadband sourcethrough a length of optical waveguide to produce an output beam,sampling sequential portions of the output beam in two dimensions byplacing an aperture in a far field of the output beam, and scanning aspatial position of the aperture relative to the output beam intwo-dimensions; and analyzing a wavelength dependence of light exitingthe aperture at a plurality of spatial sampling points using an opticaldetector with wavelength discrimination.
 2. The method of claim 1wherein the broadband source is selected from the group consisting of alight emitting diode, an amplified spontaneous emission light source, asupercontinuum light source, and any white-light source.
 3. The methodof claim 1 wherein the waveguide is the core of an optical fiber.
 4. Themethod of claim 1 wherein the aperture is a single-mode fiber.
 5. Themethod of claim 1 wherein the output beam has a wavefront with curvatureand the method further comprises the step of compensating for thecurvature.
 6. The method of claim 4 wherein the aperture scans in an arcand the arc corresponds to the curvature of the optical wavefront. 7.The method of claim 6 wherein the arc is at an approximate focal lengthwith respect to an end of the optical fiber.
 8. The method of claim 5wherein the aperture scans in an x-y plane.
 9. The method of claim 8further comprising the step of compensating for a difference between thecurved wavefront and the x-y plane.
 10. The method of claim 1 whereinthe broadband source is a tunable wavelength source.
 11. The method ofclaim 1 wherein the optical detector has frequency discrimination. 12.The method of claim 11 wherein the optical detector is an opticalspectrum analyzer.
 13. The method of claim 13 wherein the opticaldetector comprises a photodiode and an electrical spectrum analyzer. 14.The method of claim 1 wherein the output beam is analyzed using aphotodiode array.
 15. The method of claim 4 further comprising the stepof reshaping the optical wavefront to produce a planar wavefront in thefar field.
 16. A method for characterizing the modes propagating in anoptical waveguide comprising the steps of: passing light from abroadband source through a length of optical waveguide to produce anoutput beam, sampling sequential portions of the output beam in twodimensions by placing an aperture in a far field of the output beam,wherein the aperture has a fixed spatial position; moving the outputbeam over the aperture; scanning the movement of the output beam; andanalyzing wavelength dependence of light exiting the aperture at aplurality of spatial sampling points using an optical detector withwavelength discrimination.
 17. The method of claim 16 wherein the stepof scanning further comprises raster scanning the movement of the outputbeam.
 18. The method of claim 16 wherein the step of moving furthercomprises the step of moving an output tip of the optical waveguide. 19.The method of claim 16 wherein the step of moving further comprises thesteps of: bouncing the output beam off a disposed mirror; and adjustinga tilt of the mirror.
 20. A method for characterizing the modespropagating in an optical waveguide comprising the steps of: passinglight from a narrow band source with a tunable wavelength through alength of an optical waveguide to produce an output beam; measuring abeam profile using a two-dimensional detector array; and analyzingwavelength dependence of the beam profile of light exiting the opticalwaveguide by: tuning the wavelength of the narrow band source; andmeasuring the beam profile at each wavelength.
 21. The method of claim20 wherein the two-dimensional detector array is a charge-coupled-devicecamera.